Energy rotational, 78 translational

Estimating the energy from translation, rotation and vibrations. 

The latter relation results from energy conservation and forbids rotational transitions when translational energy is deficient. The back processes with transfer of the rotational energy to translational energy are unrestricted. As a consequence, the lower limit of integration in Eq. (5.18) equals f — ej at j < j and otherwise it is equal to 0. It is this very difference that leads to an exact relation between off-diagonal elements of the impact operator... 

In the liquid phase, atoms and molecules still have energies of translation, rotation, and vibration, but the nearby presence of many other molecules significantly restricts their freedom of motion. In the solid phase, in contrast, atoms and molecules no longer translate freely. Each atom or molecule in a solid can vibrate back and forth but cannot easily change places with other atoms and molecules. 

Many competing effects can contribute to ligand-receptor binding free energies changes in rotational, translational, conformational, and vibrational entropy of the... 

Continuum models are being increasingly used to study protein-ligand recognition [115]. Most studies have considered series of similar ligands or protein mutants and focussed on binding free energy differences. This leads to partial cancelation of some troublesome contributions, especially rotational/translation/vibrational entropy... 

An increase in the number of ways to store energy increases the entropy of a system. Thus, an estimate of the pre-exponential factor A in TST requires an estimate of the ratio g /gr. A common approximation in evaluating a partition function is to separate it into contributions from the various modes of energy storage, translational (tr), rotational (rot), and vibrational (vib) ... 

Molecules translate, rotate and vibrate at any temperature (except absolute zero), jumping between the requisite quantum-mechanically allowed energy levels. We call the common pool of energy enabling translation, rotation and vibration the thermal energy . In fact, we can now rephrase the statement on p. 34, and say that temperature is a macroscopic manifestation of these motions. Energy can be readily distributed and redistributed at random between these different modes. 

Heating regime Surface temp, (mean) Translational energy Rotational energy Vibrational energy Residence time(ps)... 

A molecule vibrationally excited by absorption of a laser photon can convert its excitation energy into translational (F - T transfer), rotational (F-> i ), vibrational (V- F) or even electronic energy (F- ) of the collision partners. 

The mean energy of rotation will necessarily by the laws of equi-partition of energy be equal to the mean energy of translation. 

From a theoretical perspective, isotope effects are fairly trivially computed. The stationary points on the PES and their electronic energies are independent of atomic mass, as are the molecular force constants. Thus, one simply needs to compute the isotopically dependent zero-point energies and translational, rotational, and vibrational partition functions, and evaluate Eq. (15.33). 

However, we have already worked out simple expressions for the internal energy for translational (Eq. 8.80), rotational (Eq. 8.81 or 8.82), and vibrational (Eq. 8.84) degrees of freedom. We can substitute these expressions into Eq. 8.122 and take the temperature derivative readily. 

With each electronic state, we have a series of vibration-rotation levels. See Fig. 4.3. The total molecular energy (excluding translation) for a given state of electronic and nuclear motion is the sum of the equilibrium electronic energy Ue, the vibrational energy vib, and the rotational energy... 

To get the total energy (excluding translational energy) of a polyatomic molecule in a given state of nuclear and electronic motion, we add the equilibrium electronic energy Ue and the rotational energy to (6.56) ... 

A correct understanding of the ice-water transition came when it was recognized that when ice melts not only does H increase by 6.008 kj mol-1, as the molecules acquire additional internal energy of translation, vibration, and rotation, but also the molecules become more disordered. Although historically entropy was introduced in a different context, it is now recognized to be a measure of "microscopic disorder." When ice melts, the entropy S increases because the structure becomes less ordered. 

Contrary to a conclusion (315) that CN carries most of the excess energy as translational energy, Ling and Wilson (638) have found that CN radicals are produced in two different internally excited states, one probably in the <42n state (60%) and the other in the vibrationally and rotationally excited... 

McKean 182> considered the matrix shifts and lattice contributions from a classical electrostatic point of view, using a multipole expansion of the electrostatic energy to represent the vibrating molecule and applied this to the XY4 molecules trapped in noble-gas matrices. Mann and Horrocks 183) discussed the environmental effects on the IR frequencies of polyatomic molecules, using the Buckingham potential 184>, and applied it to HCN in various liquid solvents. Decius, 8S) analyzed the problem of dipolar vibrational coupling in crystals composed of molecules or molecular ions, and applied the derived theory to anisotropic Bravais lattices the case of calcite (which introduces extra complications) is treated separately. Freedman, Shalom and Kimel, 86) discussed the problem of the rotation-translation levels of a tetrahedral molecule in an octahedral cell. 

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